Optical logic device for processing optical signals

ABSTRACT

An optical logic device has a first mirror confronting a second mirror, and a saturable absorber located between the mirrors. Radiation that is output from the device is output via the first mirror. The reflectivity of the first mirror is such that, in use, for incident radiation which has an intensity that is above a given value, the intensity of exiting radiation is below a threshold. For incident radiation that is below the given value, the intensity of exiting radiation is above the threshold.

RELATED APPLICATIONS

This application claims priority from the foreign application havingserial number PCT/EP2007/057922 and entitled “Optical Logic Device.”That application was filed on Jul. 31, 2007, and is incorporated hereinby reference in its entirety.

TECHNICAL FIELD

The present invention relates to optical logic devices.

BACKGROUND

Logical operations performed in the optical domain are required toenable ultra-fast all-optical signal processing (AOSP) for nextgeneration all-optical networks. All-optical logic gates can be used toperform many functions for AOSP for packet-switched networkapplications. These functions include header recognition and/ormodification, packet contention, data encoding, realization of half- andfull-adders, etc. Semiconductor devices offer the advantage of compactsize, low operating power, and relatively high speed.

Up to now, a number of schemes have been proposed to implement differentall-optical logical gates exploiting nonlinear effects in optical media.For instance, different logical operators have been implemented in theoptical domain exploiting Semiconductor Optical Amplifiers (SOAs). Thiscan be seen in a variety of articles such as “All-Optical Multiple LogicGates With XOR, NOR, OR, and NAND Functions Using Parallel SOA-MZIStructures: Theory and Experiment” by J. Y Kim et. al., in J. Lightw.Technol., Vol. 24, no 9, September 2006; “An All-Optical XOR Logic Gatefor High-Speed RZ-DPSK Signals by FWM in Semiconductor OpticalAmplifier” by N. Deng et. al., in J. Sel. Topics. Quant. Electron. Vol.12, no. 4, July/August 2006; and “All-optical NAND gate using cross-gainmodulation in semiconductor optical amplifiers” by S. H. Kim et. al., inElectron. Lett., vol. 41, no. 18, September 2001, all of which areincorporated herein in by reference in their entirety.

Beside SOAs, passive devices are attractive since they are cheaper anddo not usually need external circuitry for current sinking and thermalstabilization. Passive saturable absorbers (SAs) comprised ofsemiconductor multiple Quantum wells (MQWs) have been widely exploitedto perform ultra-fast AND operation. This can be seen, for example, in“1 Tbit/s demultiplexing using low temperature grown InGaAs/InAlAsmultiple quantum wells” by H. Kobayashi in Electr. Lett. Vol. 34, pp.908-909, April 1998, which is incorporated herein by reference in itsentirety.

Logical operations for AOSP in Microring Resonators (MRs) have been alsotheoretically and experimentally investigated. This is seen in thearticles entitled “40-Gb/s NRZ and RZ Operation of an All-Optical ANDLogic Gate Based on a Passive InGaAsP/InP Microring Resonator” by S.Mikroulis in J. Lightw. Technol., vol. 24 no. 3, March 2006; and“All-Optical AND/NAND Logic Gates Using Semiconductor Microresonators byT. A. Ibrahim” et. al. in Photon. Technol. Lett., vol. 15, no 10,October 2003. Both of these references are incorporated herein byreference in their entirety.

Implementation based on SOAs are usually power-consuming andintrinsically noisy, and their cascadability is limited by the amplifiernoise figure. Furthermore, in many cases they need careful polarizationalignment of the input signals. On the other hand, the nonlinearcharacteristic of a passive SA, exhibiting low transmittance at lowinput energy and high transmittance at high input power is suitable toperform only AND operation between incident optical signals.Implementation of microring resonator devices is limited bytechnological issues that make this solution at the moment still costlyand poorly reliable.

SUMMARY

According to a first aspect of the invention there is provided anoptical logic device as claimed in claim 1.

One embodiment of the invention may be viewed as an optical device whichuses saturable absorption in semiconductor Multiple Quantum Wellsembedded in an asymmetric Fabry-Perot cavity, designed to perform NANDand NOR logical operations. The device works in reflection, i.e. theoutput light is collected from the same side as the input light. Byproperly designing the cavity parameters, the device can exhibit aninverse saturable absorber behavior, i.e. high reflectivity at low inputenergy and low reflectivity at high input energy level. The device ispassive, compact, and polarization independent.

According to another aspect of the invention there is provided a methodof processing optical signals using the device of the first aspect ofthe invention.

BRIEF DESCRIPTION OF THE DRAWINGS

Various embodiments of the invention will now be described, by way ofexample only, with reference to the accompanying drawings in which:

FIG. 1 illustrates a schematic cross-sectional view of an optical logicdevice.

FIG. 2 illustrates a graphical representation of the reflectivitycharacteristic vs. normalized input energy for the device of FIG. 1,which is designed to meet an impedance matching condition at low inputenergies.

FIG. 3 illustrates a graphical representation of the reflectivitycharacteristic vs. normalized input energy for the device of FIG. 1,which is designed to meet impedance matching condition at high inputenergies.

FIG. 4 illustrates the nonlinear reflectivity characteristic of thedevice of FIG. 1 exhibiting inverse saturable behaviour, in whichdifferent values of round-trip non-saturable losses α_(ns)*d areconsidered.

FIG. 5 illustrates a schematic representation of an optical signalprocessing arrangement comprising the device of FIG. 1.

FIG. 6A illustrates a graphical representation of the reflectivityversus optical input power of the device of FIG. 1 functioning as a NANDgate.

FIG. 6B illustrates a graphical representation of the reflectivityversus optical input power of the device of FIG. 1 functioning as a NORgate.

FIG. 7A illustrates a graphical representation of spectral reflectivityof the device of FIG. 1 under different input power conditions for aNAND operation.

FIG. 7B illustrates a graphical representation of spectral reflectivityof the device of FIG. 1 under different input power conditions for a NORoperation

FIGS. 8A-8C illustrates three pairs of graphical representations of thereflectivity versus a ratio of an input power component and thesaturation power.

FIG. 9 illustrates a graphical representation illustrating intensitycharacteristics (output intensity versus input intensity) for bistableand non-bistable behaviors of the device of FIG. 1.

FIG. 10A illustrates two graphical representations of the effect of pumpdetuning on the induced reflectivity at resonance, for the device ofFIG. 1 with a moderate value of high-energy finesse (α_(ns)d=0.005), andmoderate biasing probe field (P_(pb)=P_(sat)), the value of α₀d being0.25.

FIG. 10B shows a graphical representation of reflectivity-vs-probe powercharacteristic (in absence of pump field).

FIGS. 11A-11C illustrate three graphical representations of the twoinput pump signals and the output signal for dynamic NAND operation ofthe device of FIG. 1 in the case of FIG. 10A (solid line).

FIGS. 12A-12C illustrate three graphical representations of the twoinput pump signals and the output signal for the dynamic NAND operationof the device of FIG. 1 with the same parameters as FIG. 10A (solidline), but with increased biasing probe power P_(pb)=2*P_(sat),

FIG. 13 illustrates a graphical representation of induced reflectivityat resonance by a pump field tuned 1 nm away from resonant wavelength,α_(ns)d=2.5*10⁻³, α₀d=0.25. The solid line illustrates the top mirrorreflectivity satisfying impedance matching at high energy,R_(t)=exp(−α_(ns)*d). The dashed line illustrates the top mirrorreflectivity decreased to R_(t)=96%. The bias probe power in both casesis chosen to avoid hysteresis.

FIGS. 14A-14C illustrate graphical representations corresponding to thedynamic NAND operation shown by the solid line in FIG. 13.

FIGS. 14D-14F illustrate graphical representations corresponding to thedynamic NAND operation shown by the dashed line in FIG. 13.

FIGS. 15A-15C illustrate a NOR operation with vertical-cavitysemiconductor gate (VCSG) parameters used for the dashed line of FIG.13.

DESCRIPTION

FIG. 1 shows a vertical-cavity semiconductor gate (VCSG) device 1comprising an asymmetric Fabry-Perot cavity or etalon which is formedbetween a bottom semiconductor mirror M2, whose reflectivity R_(b)approaches 100%, and a top mirror M1 with a reflectivity R_(t). The topmirror reflectivity R_(t) is lower than 100%. Each mirror can beimplemented with multiple alternating layers of two differentsemiconductor or dielectric materials, or, in the case of the highlyreflective bottom mirror, with a thin layer of metallic material (e.g.silver, or gold). Saturable losses in the cavity are provided bysemiconductor Multiple Quantum Wells (MQWs). Alternatively, other mediaexhibiting optically saturable losses can be exploited, likequantum-dots saturable absorbers or carbon-nanotube saturable absorbers,for example. The nonlinear cavity exhibits a minimum of the reflectivityat each Fabry-Perot cavity resonant wavelength. Henceforward resonantwavelength will be considered as the optimal working condition. At theresonant wavelength the VCSG reflectivity is given by “Design andoperation of antiresonant Fabry-Perot saturable semiconductor absorbersfor mode-locked solid-state lasers,” by L. Brovelli et. al., in J. Opt.Soc. Am. B 12, 311-(1995), which is incorporated herein by reference.

$\begin{matrix}{R = \frac{{{\sqrt{R_{t}} - {\sqrt{R_{b}}{\exp\left( {{- \alpha} \cdot d} \right)}}}}^{2}}{\left( {1 - {\sqrt{R_{t}R_{b}}{\exp\left( {{- \alpha} \cdot d} \right)}}} \right)^{2}}} & (1)\end{matrix}$where d[m] is the length of the absorbing layer, and α[m⁻¹] is thesingle-pass intensity absorption coefficient, which incorporates bothsaturable and non-saturable absorption contributions. Here, thesaturable part of absorption is the energy-dependent part of absorption,which is caused by the band-filling effect in the MQWs, and can beexpressed as:

$\begin{matrix}{\alpha_{sat} = \frac{\alpha_{0}}{1 + {E/E_{sat}}}} & (2)\end{matrix}$with α₀ [m⁻¹] being the unsaturated MQWs absorption coefficient, andE_(sat) the MQWs absorption saturation energy. On the other hand, thenon-saturable part of absorption α_(ns) [m⁻¹] does not change withincident energy (or intensity) and is due to fixed losses in theabsorbing material. Thus, the total absorption coefficient can beexpressed in the usual notation:

$\begin{matrix}{\alpha = {{\alpha_{n\; s} + \alpha_{sat}} = {\alpha_{n\; s} + \frac{\alpha_{0}}{1 + {E/E_{sat}}}}}} & (3)\end{matrix}$

Using eq. (1), we can see that the device reflectivity is zero ifR _(t) =R _(b)exp(−2αd)  (4)where the quantity exp(−2αd) is the round trip power transmissionthrough the absorber structure. The condition expressed by eq. (4) isusually called impedance-matching (IM). The internal roundtrip lossesdepend on the input energy via the nonlinear absorption coefficient α,as expressed by eq. (3). Thus, for a given R_(t), IM condition issatisfied for a particular value of the signal energy. By substituting(2) into (3), the energy-dependent impedance-matching condition becomes:R _(t) =R _(b)exp−2[α_(ns) d+α ₀ d/(1+E/E _(sat))d]  (5)

When the top mirror reflectivity R_(t) satisfies the condition:R _(t) =R _(b)exp−2[(α_(ns)+α₀)d]  (6)the IM-condition is satisfied at low input energy (E<<E_(sat)), as canbe seen from eq. (5). This the optimal condition for having anall-optical AND gate, in which the resonator enhances the typical SAcharacteristic. In this case indeed, the VCSG reflectivity (which is ameasure of the intensity of the light exiting the device via the topmirror M1, and is defined as the ratio of the exiting intensity and theentering intensity) is low (ideally zero) for low input powers, and highfor high input powers. A typical characteristic of the VCSG reflectivityvs. normalized input energy is shown in FIG. 2, obtained from numericalsimulations.

On the other hand, if the top mirror reflectivity R_(t) satisfies thecondition:R _(t) =R _(b)exp(−2α_(ns) d)  (7)the minimum of reflectivity (i.e. the impedance matching condition) isachieved at high input energy (E>>E_(sat)), as can be easily verifiedfrom eq. (5). In this case the VCSG exhibits an inverse saturableabsorber characteristic, as it is demonstrated in the following.

Assuming R_(b)≅1, under the condition expressed by eq. (6), at low inputenergies (E>>E_(sat)) the VCSG reflectivity is given, from eq. (1):

$\begin{matrix}{R_{ON} = \frac{{{\mathbb{e}}^{{- 2}\alpha_{n\; s}d}\left\lbrack {1 - {\mathbb{e}}^{{- \alpha_{0}}d}} \right\rbrack}^{2}}{\left\lbrack {1 - {\mathbb{e}}^{{- {({{2\alpha_{n\; s}} + \alpha_{0}})}}d}} \right\rbrack^{2}}} & (8)\end{matrix}$which expresses the high-reflectivity (ON) state of the gate. The valueof R_(ON) depends on the values of α₀ and α_(ns). For high levels of theinput power (E>>E_(sat)), the saturable part of the absorption iscompletely bleached (i.e. α_(sat)˜0, there are substantially nosaturable losses left as an effect of the high incident energy), and theabsorption coefficient given by eq. (3) becomes:α=α_(ns)  (9)Under the condition expressed by eq. (7), we have that the reflectivityof the VCSG, given by eq. (1) and assuming R_(b)=1, drops to R_(Off)=0,since the device is now impedance-matched.

Results of numerical simulation for the case of a VCSG designed to meetimpedance matching condition at high input energies are shown in FIG. 3.

Thus, by matching the impedance of the VCSG (hence cancelling thereflected field) when the saturable part of absorption is completelybleached, it is possible to reverse the AND characteristic of a standardsaturable absorber. This feature allows the implementation of NOR/NANDlogical gates, as explained in more detail below. This functionality canbe achieved by carefully selecting the reflectivity of the top mirrorM1. From eq. (6) and eq. (7), it can be seen that the condition forhaving a NAND/NOR gate corresponds to a higher top mirror reflectivityR_(t) with respect to the case of an AND gate.

Optimizing Design

As seen from above, by matching the impedance of the VCSG (hencecancelling the reflected field) when the saturable part of absorption iscompletely bleached, it is possible to reverse the AND characteristic ofa standard SA.

However, in order to implement effective logical operations a step-liketransition, with a reduced dynamic range required for switching the gatebetween the ON and the OFF states, is desirable. In order to obtain asteep transition of the inverse saturable absorber characteristic, theinternal field enhancement effect inside the resonator can be exploited,which is related to the cavity finesse. The higher the cavity finesse,the higher the field enhancement factor. Since the cavity finesse alsovaries dynamically according to the power-dependent value of theabsorption coefficient, it is important to have a finesse which is asmuch as possible increasing during the transition. At resonance,intensity distribution inside the structure can be much higher (orlower) than the input energy, depending on working conditions. The ratiobetween the energy inside the cavity and the energy incident on it atthe resonant wavelength is given by “Design and operation ofantiresonant Fabry-Perot saturable semiconductor absorbers formode-locked solid-state lasers,” by L. Brovelli et. al., in J. Opt. Soc.Am. B 12, 311-(1995).

$\begin{matrix}{\psi = {\frac{\left( {1 - R_{t}} \right)}{\left( {1 - {\sqrt{R_{t}R_{b}}{\exp\left( {{- \alpha}\; d} \right)}^{2}}} \right.} = \frac{{{??}^{2}\left\lbrack {1 - {\sqrt{R_{t}R_{b}}{\exp\left( {{- \alpha}\; d} \right)}}} \right\rbrack}\left( {1 - R_{t}} \right)}{\pi^{2}\sqrt{R_{t}R_{b}}{\exp\left( {{- \alpha}\; d} \right)}}}} & (10)\end{matrix}$

Being ℑ, the resonator finesse, is defined as:

$\begin{matrix}{{??} = \frac{{\pi\left\lbrack {\sqrt{R_{t}R_{b}}{\exp\left( {{- \alpha}\; d} \right)}} \right\rbrack}^{1/2}}{1 - {\sqrt{R_{t}R_{b}}{\exp\left( {{- \alpha}\; d} \right)}}}} & (11)\end{matrix}$

It is well known that the finesse of a Fabry-Perot resonator increasesif the losses inside the cavity decrease. Since the absorptioncoefficient is always decreasing for increasing power, the finesseincreases monotonically for increasing input energy, which is good forfurther pushing the absorber in the saturation regime. Indeed in thisway, once the absorption is bleached above a certain value, the internalfield increases, and this helps to bring the absorption to the finalstate more rapidly. Large changes of Ψ for small changes of the inputenergy can make possible to realize steep transition from ON-to-OFFstate. Thus, the finesse should exhibit a steep increase for aapproaching α_(ns). For E>>E_(sat), we have:

$\begin{matrix}{\psi_{E->\infty} = \frac{\left( {1 - R_{t}} \right)}{\left( {1 - {\sqrt{R_{t}R_{b}}{\exp\left( {{- \alpha_{n\; s}}d} \right)}^{2}}} \right.}} & (12)\end{matrix}$If the top mirror is optimized for impedance matching at high powers(α_(E→∞)=α_(ns)), then the previous expression can be rewritten as:

$\begin{matrix}{\psi_{E->\infty}^{IM} = {\frac{\left( {1 - {R_{b}{\exp\left( {{- 2}\alpha_{n\; s}d} \right)}}} \right.}{\left( {1 - {R_{b}{\exp\left( {{- 2}\;\alpha_{n\; s}d} \right)}^{2}}} \right.} = \frac{1}{\left( {1 - {R_{b}{\exp\left( {{- 2}\alpha_{n\; s}d} \right)}}} \right.}}} & (13)\end{matrix}$And it can be seen that for R_(b)=1 and α_(ns)→0 then Ψ→∞. Hence, smallvalues of α_(ns) are good to have a high value of the internal fieldenhancement factor when the absorber is completely (or partially)saturated. This decreases the dynamic input energy range for which thegate changes its operating state, allowing a steep characteristic ofgate reflectivity as a function of the input energy. FIG. 4 illustratesthe effect of decreasing α_(ns) (for a fixed value of α_(ns)) on thenonlinear reflectivity characteristic of the VCSG. The results showingthe nonlinear VCSG reflectivity at a cavity resonance as a function ofinput energy of a signal tuned at the resonant wavelength. Bottom mirrorreflectivity R_(b) is assumed to be 100%.Design of NOR/NAND Logical Operators with VCSG

Up to now, the incident field tuned at one of the resonances of the VCSGhas been considered. However, if it is desired to use the VCSG for NORand NAND logical operations, a pump-probe configuration is required. Inparticular, two pump beams representing the two logical inputs wouldaffect the probe signal state at the VCSG output, providing the resultof the logical operations between two input pump bits. In principle boththe pump signals and the probe signal could be tuned at two differentresonances of the nonlinear cavity. In this case the efficiency of theoperation would be increased up to its maximum value. In practice, it issufficient and also desirable that only the probe signal is tuned at aFabry-Perot resonance, while the two pumps could be tuned away from theprobe wavelength. This would increase wavelength transparency of thedevice with respect to external input pump signals, while a local probesignal wavelength is kept close to a VCSG resonance.

Thus, in order to implement NAND/NOR functions in a pump-probeconfiguration, a spectral analysis of the gate is required. This can beeasily done by considering the general expressions for the reflectivityof the VCSG and the internal field enhancement factor that, for an inputsignal matching a cavity resonance are given by eq. (1) and (6). Bytaking into account the round-trip phase in the resonator associatedwith any input wavelength eqs. (1) and (6) can be extended to:

$\begin{matrix}{R = \frac{\left\lbrack {\sqrt{R_{t}} - {\sqrt{R_{b}}{\exp\left( {{- \alpha}\; d} \right)}}} \right\rbrack^{2} + {4R_{t}R_{b}{\exp\left( {{- \alpha}\; d} \right)}{\cos^{2}\left( {\phi/2} \right)}}}{\left\lbrack {1 - {\sqrt{R_{t}}\sqrt{R_{b}}{\exp\left( {{- \alpha}\; d} \right)}}} \right\rbrack^{2} + {4R_{t}R_{b}{\exp\left( {{- \alpha}\; d} \right)}{\cos^{2}\left( {\phi/2} \right)}}}} & (14) \\{\Psi = \frac{1 - R_{t}}{\left\lbrack {1 - {\sqrt{R_{t}}\sqrt{R_{b}}{\exp\left( {{- \alpha}\; d} \right)}}} \right\rbrack^{2} + {4R_{t}R_{b}{\exp\left( {{- \alpha}\; d} \right)}{\cos^{2}\left( {\phi/2} \right)}}}} & (15)\end{matrix}$in which φ is the wavelength dependent single-pass dephasing. By usingeqs (10) and (11) and the power dependence of a expressed by eq. (2)(with E=ΨE_(in), being E_(in) the input energy) it is possible tocalculate the reflectivity spectrum of the VCSG for different values ofthe input pump and probe energy. By means of the spectral model ispossible then to calculate the effect of the pump power at a genericwavelength on the reflectivity experienced by a probe field tuned at theresonant wavelength. A signal processing apparatus, including the device1, is shown in FIG. 5.NAND Operation

A schematic representation of the operation principle of the NAND gatewith the proposed VCSG is illustrated in FIG. 6A, showing thereflectivity experienced by the probe field at resonance as a functionof total input power (probe and pump fields). Let us consider an idealgate, with an almost step-like inverse SA reflectivity characteristic. Acontinuous probe field with power P_(pb), close to the transition edge,is first applied to the gate, experiencing high reflectivity in absenceof pump pulses, R(P_(pb)).

The two pump signals are considered to be applied simultaneously to thedevice. The pump signal is comprised of logical “1” and “0” signals,where the pump power associated with each “1” data signal is P_(pmp) andthe pump power associated with a “0” data signal is zero. The value ofboth P_(pb) and P_(pmp) are chosen in such a way that a single pump “1”data signal is not enough to switch the gate in the OFF state(corresponding to low reflectivity for the probe light), while twice thepower associated with a pump “1” signal is enough to switch the gate inthe OFF state. Thus, the reflectivity R(P_(pb)+P_(pmp)) associated withthe sum of probe power and a single pump bit is high. On the other handR(P_(pb)+2P_(pmp)), corresponding to a total input power given by thesum of probe and two pump “1” data signals is low. The filtered outputprobe field represents hence a NAND operation between the two input pumppulse pulses. The calculated spectral reflectivity of the nonlinear gateunder different input power conditions, are shown in FIG. 7A, for thecase of NAND operation. The parameters value used in the simulationsare: α₀d=0.25, α_(ns)d=0.005 P_(pb)=2.5*P_(sat), P_(pmp)=1*P_(sat), andpump detuning from resonance Δ_(res)=1 nm.

With opportune values of input probe and pump powers, it can be seenthat with the reflectivity is always high when either the probe field orthe probe and a single pump pulse are applied to the gate. On the otherhand, if twice the pump power is applied to the gate the reflectivity atthe resonant wavelength is drastically reduced. From FIG. 7A it can alsobe seen that the resonance width changes drastically between thelow-finesse regime in the ON state and the OFF state associated to ahigh value of the resonator finesse. The bandwidth of the VCSG resonancein the OFF state is thus inversely proportional to the steepness of thenonlinear characteristic. Increasing the bandwidth would decrease thesteepness of transition, leading to a reduced ON/OFF Extinction Ratio(ER). A trade-off between resonance bandwidth and ER has to beconsidered in designing the device. The simulation also revealed that inmost cases ER greater than 10 dB can be obtained with resonancebandwidths wide enough to allow operation speeds exceeding tens of GHz.

NOR Operation

In a similar way NOR operation can be performed. In this case, with aprobe field matching a cavity resonance and with a proper power value,if one single pump pulse contains enough energy to turn the gate in theOFF state at the resonant wavelength, NOR between the two pump pulsescan be retrieved by filtering out the reflected probe power. Theschematic of the operation and the calculated spectral reflectivity forthis case are shown in FIG. 6B and FIG. 7B, respectively. The parametersused to calculate the spectral reflectivity are the same as in the caseof FIG. 7A, with the exception of pump power, set to P_(pmp)=2*P_(sat),in this case.

Thus, by properly setting the pump power (with an opportune biasingprobe power level) the two operations can be obtained in the samedevice. In an alternative embodiment, the biasing probe power is changedwhile keeping constant the pump power to switch between the two logicaloperations of NAND and NOR.

Effect of Cavity Parameters

In this section the effects of cavity parameters on device operation areinvestigated. In particular, the effect of the saturable low-powerabsorption coefficient α₀ and the non-saturable absorption coefficient,α_(ns), on the nonlinear cavity characteristic are analysed. The bottommirror reflectivity was assumed to be 100%, and the top mirrorreflectivity was set to the value satisfying condition (4). All theresults are normalized to the absorber saturation power.

The figures of merit of the device are the ON/OFF contrast ratio, thedynamic energy range in which the transition take place, and theefficiency of the gate, i.e. the reflectivity value when the gate is inthe ON state.

Since the device is intended to operate in a pump-probe operation, thenonlinear reflectivity at the resonant wavelength as induced by theprobe field itself was first calculated. This simulation permitted theassessment of an appropriate value for the input probe power. In asecond step, the reflectivity experienced by the probe field (always atresonance), with a suitable power level was calculated as a function ofpump power, being pump light at a fixed detuning from resonance. Thesimulations were performed by means of the nonlinear spectral modelintroduced above.

FIGS. 8A, 8B, and 8C show the results of the simulations. Each pair offigures represents the nonlinear reflectivity at resonance, induced bythe probe (upper plots) and the pump field (lower plots), for a chosenvalue of probe power, obtained for three different values of α_(ns)d,for a fixed value of α₀d. It can be seen from the Figures that thesteepest characteristic of reflectivity at resonance vs. pump power canbe obtained for the smallest value of α_(ns)d. The reason for this, asexplained above, lies in the steep increase in the resonator finesse asthe losses are saturated beyond a certain value. Consequently, the probefield power inside the resonator is enhanced, which contributes to adeeper saturation of the absorber, leading to even higher value finessesand of the field enhancement factor at resonance. Under theseconditions, it is the probe light itself that contributes to a fastswitch of the gate from ON to OFF state, once the initial condition ofhigh reflectivity is modified by external pump signals. In theseoperating conditions the role of the pump power can be seen to be thetrigger of a regenerative process for the probe light at the resonantwavelength. However, in this particular situation optical bistabilitycould appear. That is, when the pump field is switched off, the devicecould remain in the OFF state. Although it could be useful in othersystem applications, this is clearly a situation that should be avoidedfor this kind of application.

Returning to FIGS. 8A-8C it can be seen from thereflectivity-vs.-P_(pmp) characteristic that complete transition fromON-to-OFF state, could be attained in a reduced dynamic range of inputpump power. The smallest dynamic range occurs for the lowest values ofα_(ns)d. However, very small values of the non-saturable losses α_(ns)dalso lead to unpractical values of top mirror reflectivity (>0.99). Thiscould in principle prevent practical implementation of the device.Furthermore, as is discussed below, in this situation it is more likelyto have bistability. Increasing the non-saturable losses α_(ns)d has atwofold detrimental effect. The non linear characteristic at resonancevs. pump power becomes smoother and the ON/OFF contrast ratio isdegraded. Also these behaviours can be explained within Fabry-Perottheory. If the saturable part of the losses (α₀d, in the slide legend)is decreased, the detrimental effects of non negligible α_(ns) is evenworse. On the other hand, increasing α₀d leads to good extinction ratiovalues even in presence of moderate values of α_(ns)d. However, veryhigh values of α₀d are difficult to obtain in practice, lead to highvalues of saturation power (hence preventing low-power operation) andusually came along with higher values of α_(ns). A trade-off for deviceperformance for practical implementation should hence be considered.

Bistability Analysis

Here, bistability operation of the device is investigated, together withconditions for avoiding bistability. The analysis of bistability can bemade by using a procedure similar to that of “Criteria for opticalbistability in a lossy saturating Fabry-Perot” by E. Garmire in J.Quant. Electron., vol. 25, no. 3, March 1989, which is incorporatedherein by reference in its entirety., in which the nonlinear effect wasonly associated to refractive index change, rather than absorption. Herewe neglect the nonlinear index change (assumed to be small with respectto large absorption changes), while considering only the effects ofsaturation of absorption. The analysis could be easily extended to thegeneric case in which both nonlinear index and absorption change aretaken into account. Bistability behavior can be seen by writing both theinput and reflected intensities (I_(in) and I_(ref), respectively) as afunction of the field intensity inside the cavity I_(c), and thenplotting I_(ref) against I_(in), ignoring the variable I_(c). We have:

$\begin{matrix}{I_{i\; n} = {I_{c}\frac{\left( {1 - {\sqrt{R_{t}}\sqrt{R_{b}}{\mathbb{e}}^{{- {({\frac{\alpha_{o}}{1 + {{Ic}/I_{s}}} + \alpha_{n\; s}})}}d}}} \right)^{2}}{\left( {1 - R_{t}} \right)}}} & (16) \\{I_{r} = {I_{c}\frac{\left( {\sqrt{R_{t}} - {\sqrt{R_{b}}{\mathbb{e}}^{{- {({\frac{\alpha_{o}}{1 + {{Ic}/I_{s}}} + \alpha_{n\; s}})}}d}}} \right)^{2}}{\left( {1 - R_{t}} \right)}}} & (17)\end{matrix}$

FIG. 9 shows the input light-reflected light characteristic at resonancefor different values of α_(ns)d and fixed α₀d. It can be seen that inthe case of higher finesse at high input energy (lower α_(ns)d), thedevice exhibits a bistable behaviour. From above it was shown that thecondition of high finesse for high input energy leads to the steepestpossible transition between ON and OFF state. However, bistability setsa limit to the ideal minimum value of internal non-saturable losses. Infact, if the bistability conditions are met, depending on the inputprobe biasing power, once the pump signal is switched off the devicecould remain in the OFF state rather than going back to its initial ONstate. This is also confirmed by dynamic simulations presented below. Indesigning the cavity, the condition for bistability setting should beavoided. This could be made basically in two ways. The first one is todesign a cavity which is inherently non-bistable. The second one is tobias the gate with a proper value of input probe power that lies outsidethe histeresis region comprised between the dashed lines of FIG. 9. Boththese methods show some drawback in terms of the ON/OFF extinction ratiodegradation. These effects are discussed, together with some possiblemitigating solutions below, when presenting the results of numericalsimulations relative to dynamic behaviour of the VCSG.

Dynamic Operation

The dynamic operation of the VCSG can be investigated by inserting ineq. (1) the equation governing the dynamic variation of absorption inthe MQWs. By using a single-time constant model for the absorbingsection we can write for the absorbing coefficient inside the cavity:

$\begin{matrix}{\frac{\mathbb{d}\alpha}{\mathbb{d}t} = {\frac{\alpha_{0} - \alpha}{\tau_{s}} - \frac{\left( {1 - R_{t}} \right) \cdot P_{pb} \cdot \alpha}{\begin{matrix}{{E_{sat}\left( {1 + {{\sqrt{R_{t}} \cdot \sqrt{R_{b}}}{\mathbb{e}}^{{- {({\alpha + \alpha_{n\; s}})}}d}}} \right)}^{2} -} \\{4{\sqrt{R_{t}} \cdot \sqrt{R_{b}}}{\mathbb{e}}^{{- {({\alpha + \alpha_{n\; s}})}}d}{\cos^{2}\left( {\phi_{pb}/2} \right)}}\end{matrix}} - \frac{\left( {1 - R_{t}} \right) \cdot P_{pmp} \cdot \alpha}{{E_{sat}\left( {{1 + \sqrt{R_{t}}}{\cdot \sqrt{R_{b}} \cdot {\mathbb{e}}^{{- {({\alpha + \alpha_{n\; s}})}}d}}} \right)}^{2} - {4{\sqrt{R_{t}} \cdot \sqrt{R_{b}}}{\mathbb{e}}^{{- {({\alpha + \alpha_{n\; s}})}}d}{\cos^{2}\left( {\phi_{pmp}/2} \right)}}}}} & (18)\end{matrix}$where P_(pb) and P_(pmp) are the usual probe and pump input powers,respectively, and φ_(pb) and φ_(pmp) are the round-trip phasesassociated with probe and pump wavelength, respectively, and τ_(s) isthe carrier recombination time in the MQWs. In the following a value ofτ_(s)=5 ps was assumed. This value can be typically reached insemiconductor MQWs by using standard techniques for speeding uprecombination time in semiconductor materials, like for instance ionimplantation as described by P. W. Smith et. al., in “Mode locking ofsemiconductor diode lasers using saturable excitonic nonlinearities,”published in J. Opt. Soc. Amer. B, Opt. Phys., vol. 2, no. 7, pp.1228-1236, July 1985, or of low-temperature molecular beam epitaxy asdescribed by R. Takahashi et. al. in “Ultrafast 1.55 μm photoresponsesin low-temperature-grown InGaAs/InAlAs quantum wells,” published inAppl. Phys. Lett., vol. 65, no. 14, pp. 1790-1792, October 1994. Both ofthese documents are incorporated herein by reference in their entirety.NAND Operation

As noted above, in order to allow recovery of the gate to its initialstate, condition for hysteresis in the cavity should be avoided. Thiscould be made by limiting the finesse value at high energies, bychoosing a value for α_(ns) sufficiently large, or by setting thebiasing probe power lying outside the histeresis bounding region. Ofcourse, the two solutions can be also combined. However, both thesesolutions infer the quality of the output signal. Indeed, increasing thevalue of α_(ns), smoothes the On/Off transition at the resonantwavelength, as illustrated in FIG. 10A. The curve becomes even smootherif we consider the reflectivity change of the probe field that isinduced by a pump field away from resonance (see, for example FIG. 8C,lower plot, solid line). This degradation could eventually prevent theoperation of the NAND gate, in which a strong reflectivity change isrequired within 3-dB of input pump dynamic range. A possible solutionwould be in this case to tune also the pump field in proximity of acavity resonance. In this case the steepness of transition can bepreserved, provided that α_(ns) is not too large and NAND operation canstill be possible. An example of this situation is shown in FIG. 10A,where the reflectivity of the probe field induced by the pump field forthe two cases of a pump far (dashed line) and near (solid line) a secondcavity resonance are shown, respectively, with α_(ns)d=5⁻³, andα₀d=0.25. In this case the probe biasing power is also chosen to beP_(pb)=P_(sat), not too close to the transition edge of thereflectivity-vs.-probe power characteristic (shown in FIG. 10B). Thedynamic behavior, obtained using the model given eqs. (14) and (1) isalso shown in FIGS. 11A-11C. For comparison, FIGS. 12A-12C illustratethe dynamic behavior in the case of bistable operation. In this case theprobe power is increased up to 2*P_(sat), and it can be seen from thelowermost graph (FIG. 12C) that in this case the output probe powerremains low even after the pump pulses have been switched off. Thecondition of having a pump field close to the cavity resonance may notbe desirable, since it would limit the transparency of the operation toexternal pumps wavelength, unless a wavelength converting stage would beinserted at device input.

To allow tolerance to pump detuning from resonance, and avoidhysteresis, it is then possible to choose low values of α_(ns)d and setthe bias power not too close to the transition edge. If the reflectivityof the probe induced by the pump power in this case is considered, thedegradation of the characteristic is again observed.

This is shown in by the solid line in FIG. 13 where it can be seen that,for a probe power sufficiently low to avoid bistability, thereflectivity change at resonance induced by a pump field detuned by 1nm, exhibit a smooth slope in proximity of low reflectivity values (highinput energies). Furthermore, it can also be seen that the requiredoperating power is increased. The top mirror reflectivity, in accordancewith condition given by eq. (4), is R_(t)=exp(−α_(ns)*d). Thecorresponding dynamic behavior is shown in FIGS. 14A-C. Although NANDoperation is somehow preserved, the ER of the output signal is degraded.However, this degradation could be strongly mitigated by impedancematching the gate in correspondence of a partially saturated absorptioncoefficient (α_(ns)<α<α₀+α_(ns)). Namely, the top mirror reflectivityshould be lowered below the value needed for impedance matching at highinput energy R_(t)=exp(−α_(ns)*d). The effect is shown by the dashedline in FIG. 13, where the reflectivity experienced by the probe fieldis plotted versus the pump power for a top mirror reflectivity ofR_(t)=96%. For a probe power of P_(pb)=P_(sat), the power associated toa single “1” bit pump signal can be chosen to provide high reflectivityfor the probe light, while the power associated to two input “1” bitpump signals can be chosen to lie in the low reflectivity region. Inthis way NAND operation with high ER for the filtered probe light can beobtained. The increased ER is attained at the expense of a slightlyreduced gate efficiency (lower reflectivity in the ON state). Besideincreasing output ER, lowering the top mirror reflectivity has also twoother beneficial consequences: first, it helps prevent hysteresis, sincea decreased top mirror reflectivity increases the total losses in thecavity and hence reduce its finesse. As a result, it is now possible toset probe power closer to the transition edge than what would have beenpossible with R_(t)=exp(−α_(ns)*d). Another benefit of reducing R_(t) isa dramatic decrease of input pump power required for switching the gate,since a lower value of R_(t) allows more pump field to be effectivelycoupled inside the cavity. Dynamic simulation of NAND operation relativeto the dashed line in FIG. 13 is shown in FIGS. 14D-14F. Furthermore,condition given by eq. (4) for small values of α_(ns)d lead to very highvalues of R_(t) that could result unpractical. Lowering R_(t), couldhence result also in easier mirror fabrication.

NOR Operation

Implementation of NOR operation is straightforward. For what seen, inthis case there is less constraint on the steepness of the nonlinearprobe reflectivity characteristic induced by the pump field. In thiscase, indeed, even a relatively smooth characteristic can be tolerated,provided that each pump pulse has enough power to switch the gate in theOFF state. However, low-power operation is always desirable, and we cantake advantage of the considerations developed in the previoussub-section to implement efficient, low-power, NOR gate with VCSG. As anexample, FIGS. 15A-15C show a NOR operation of the VCSG relative to thecase of the dashed line shown in FIG. 13, with a pump power rangingwithin the low-reflectivity region.

Conclusions

Advantageously, as shown above, a nonlinear VCSG comprises an asymmetricFabry-Perot resonator including nonlinear absorbing MQWs section enablesthe realisation of NAND and NOR logical operators. The device relies onthe particular design of the cavity which allows an inverse saturableabsorber characteristic to be achieved for a probe field tuned at a VCSGresonant wavelength. This is possible by matching the impedance of thegate in correspondence of the non-saturable part of the losses in thecavity. Nonlinear changes of refractive index are not considered here,since they are assumed to be small with respect to large absorptionchange in the MQWs. However, the analysis could be easily extended tothe case in which carrier density concentration-induced index change arealso taken into account. In practical applications, the carrier densitychange in the MQWs would result in a shift of the cavity resonance atsteady-state, that could be taken into account by properly tuning theinput probe field. Device performances under different cavity parametersconditions have been investigated with the steepest transitions fromON-to-OFF state being achieved, as expected, for the lowest value ofnon-saturable losses in the cavity. However, in this conditionbistability may occur, preventing device correct operation. An heuristicprocedure, investigating settling conditions for bistability was alsocarried out. Nevertheless, some simple design rules for avoidingbistability and preserve good ON/OFF extinction ratio are proposed andnumerically verified by means of a dynamic model. The advantage of thedevice for all-optical signal processing in optical networksapplications are related to its compactness, passive operation,polarization insensitivity and possibility of low-power operation.

The present invention may, of course, be carried out in other ways thanthose specifically set forth herein without departing from essentialcharacteristics of the invention. The present embodiments are to beconsidered in all respects as illustrative and not restrictive, and allchanges coming within the meaning and equivalency range of the appendedclaims are intended to be embraced therein.

1. An optical logic device comprising: a first mirror configured to receive and selectively output radiation from the optical logic device; a second mirror facing the first mirror; a saturable absorber located between the first and second mirrors, and including a saturable non-linear absorption coefficient dependent on radiation energy; the first mirror having a reflectivity such that: for all received radiation having energies above a given value, the energy of radiation output from the device will remain below a threshold; and for all received radiation having energies below the given value, the energy of exiting radiation will remain above the threshold.
 2. The device of claim 1 wherein the reflectivity of the first mirror R_(t) is substantially equal to: R_(b)exp(−2α_(ns)d) where R_(b) is a reflectivity of the second mirror, d is the distance between mirrors, and α_(ns) is a non-saturable part of the non-linear absorption coefficient.
 3. The device of claim 2 wherein the reflectivity of the second mirror is substantially equal to 100%.
 4. The device of claim 1 further comprising: first and second logic signal inputs coupled to the first mirror and configured to receive first and second input binary signals; wherein the radiation energy received by the first mirror and the reflectivity of the first mirror are configured to implement an optical NAND or NOR logical function.
 5. The device of claim 4 wherein the optical logic device is configured to receive a controlled input biasing control signal and at least two input binary signals.
 6. The device of claim 5 wherein the optical logic device is configured to implement a NAND or a NOR logical function based on an intensity of the input biasing control signal.
 7. The device of claim 5 wherein the input biasing control signal is at a cavity resonance wavelength and the input binary signals are at non-resonant wavelengths.
 8. The device of claim 1 wherein the optical logic device is configured as an asymmetric Fabry-Perot cavity.
 9. A method of operating an optical logical device comprising a first mirror configured to receive and selectively output radiation from the optical logic device, a second mirror facing the first mirror, and a saturable absorber located between the first and second mirrors, and including a saturable non-linear absorption coefficient dependent on radiation energy, the method comprising: configuring a reflectivity of the first mirror and the energy of radiation received by the first mirror such that: for all received radiation having energies above a given value, the energy of radiation output from the device is will remain below a threshold; and for all received radiation having energies below the given value, the energy of exiting radiation is will remain above the threshold.
 10. The method of claim 9 further comprising: inputting at least two binary signals and a biasing control signal to the optical logic device; and controlling relative intensities of the signals to configure the device to operate as a NAND gate or as a NOR gate. 